demo_metaanalysis.Rmd

---
title: "Meta analysis demo"
author: "Beni Stocker"
date: "12/3/2021"
output:
  html_document:
    toc: true
    toc_float: true
    code_folding: show
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE)
library(tidyverse)
library(metafor)   # see ?dat.curtis1998 for an example with CO2 manipulation data
library(patchwork)
library(ggrepel)
```


## Read data

We're reading data from Kevin's database, selecting only data where only CO2 was manipulated, from experiments that lasted more than 2 years, and include OTC and FACE experiments. This is a demo and we're using just ANPP data (any of `c("aboveground_production", "annual_aboveground_biomass_production", "ANPP")`).

```{r, warning=FALSE, message=FALSE}
df <- read_csv("~/data/gcme/data_received_190325/NewData_wide_CORRECTED2.csv") %>%
  
  # something is wrong in columns ambient_Sd, ambient_Se, elevated...
  mutate( ambient_Sd  = as.numeric(ambient_Sd),  ambient_Se  = as.numeric(ambient_Se), 
          elevated_Sd = as.numeric(elevated_Sd), elevated_Se = as.numeric(elevated_Se) )
  
# save experiments names
df_experiments <- df %>% select(exp_nam, prev_name) %>% distinct()

# take only experiments >1 yr
list_exp_gt1yr <- df %>% 
  filter(!is.na(Year)) %>% 
  group_by(exp_nam) %>% 
  summarise(nyears=max(Year)) %>% 
  filter(nyears>1) %>% 
  select(exp_nam) %>% 
  unlist() %>% 
  unname()

selvars <- c("aboveground_production", "annual_aboveground_biomass_production", "ANPP")

df_c <- df %>%
  
  ## filter experiments with only manipulated CO2
  filter(treatment=="c") %>% 
  
  ## More than 1 year data
  filter(exp_nam %in% list_exp_gt1yr) %>% 
  
  ## Combine with experiments meta info
  left_join( 
    read_csv("~/data/gcme/data_received_190325/table_var_exp_names_experiments.csv") %>% 
      select(prev_name, Fumigation_type, Vegetation_type),
    by = c("prev_name")
  ) %>% 
  
  ## Filter only Fumigation_type OTC or FACE
  filter( Fumigation_type %in% c("OTC", "FACE") ) %>%
  
  ## reduce for demo
  dplyr::select(exp_nam, factors, treatment, Data_type, Sampling_Year, ambient, ambient_Sd = ambient_Sd, ambient_Se, elevated, elevated_Sd, elevated_Se, n_plots) %>% 
  
  ## use only ANPP data
  filter(Data_type %in% selvars) %>% 
  mutate(varnam = "anpp") %>% 
  
  ## create a unique indendifying
  mutate(id = paste0("i", 1:n()))
```

The data now looks like this:

```{r}
df_c %>% 
  knitr::kable()
```


## Response ratio

Calculate log response ratio within each plot, using `metafor::escalc(measure = "ROM", ...)`.

**Questions:**

- Do you calculate the response ratio before aggregating (done in the next step)?
- I'm caluclating the standard error of the response ratio from the variance (which is returned by `escalc()`) as:

$$
SE = \frac{\sigma}{\sqrt{N}}  
$$

```{r}
df_c <- df_c %>%         
  
  mutate( 
    ambient_Sd = ifelse( is.na(ambient_Sd),  ambient_Se  * sqrt(n_plots), ambient_Sd ),
    elevated_Sd  = ifelse( is.na(elevated_Sd), elevated_Se * sqrt(n_plots), elevated_Sd )
    ) %>%

  ## Get logarithm of response ratio and its variance
  metafor::escalc( 
    measure = "ROM", 
    m1i = elevated, sd1i = elevated_Sd, n1i = n_plots, 
    m2i = ambient,  sd2i = ambient_Sd,  n2i = n_plots, 
    data=., 
    append = TRUE, var.names = c("logr", "logr_var") ) %>% 
  as_tibble() %>% 
  
  ## calculate standard error of response ratio
  mutate( logr_se = sqrt(logr_var)/sqrt(n_plots) )
```

## Aggregate

Aggregate data by experiment (and variable name - here only ANPP), pooling all measurements (multiple years, sampling dates and plots). For this we're using `MAd::agg()` with a correlation among within-study outcome variables of 0.5 (`cor = 0.5`) is assumed as per the function's default.

In the data we always have the same number of plots in ambient and elevated and calculate standard error of effect size from its standard deviation (`sqrt(logr_var)`) and N. 

```{r}
df_c_agg <- df_c %>% 
  
  filter(!is.na(logr_var) & !is.na(logr)) %>% 
  mutate( id = exp_nam ) %>% 
  
  MAd::agg( id = id, es = logr, var = logr_var, n.1 = n_plots, n.2 = n_plots, cor = 0.5, method = "BHHR", data = . ) %>% 
  
  rename(exp_nam = id,
         logr = es, 
         logr_var = var) %>% 

  ## add number of plots column and varnam
  left_join( df_c %>% 
               ungroup() %>% 
               group_by( exp_nam, varnam ) %>%
               summarise( n_plots = sum(n_plots) ) %>% 
               select( exp_nam, varnam, n_plots ),
             by = "exp_nam" ) %>% 
  
  ## calculate standard error of effect size
  mutate( logr_se = sqrt(logr_var)/sqrt(n_plots) ) %>% 
  as_tibble()
```

**Question:**

This now yields a value and standard error for each experiment. However, the output value yields identical results as values from simple aggregate by `mean()`. Shouldn't the aggregation take into account $N$ (`n_plots`) and their variances (e.g., using `metafor::rma.mv()`) for aggregation to within-study effect sizes? The code below shows a comparison of alternatives (example for DUKE data):

```{r}
## as done above
df_c %>% 
  filter(exp_nam == "DUKE") %>% 
  mutate( id = exp_nam ) %>% 
  MAd::agg( id = id, es = logr, var = logr_var, n.1 = n_plots, n.2 = n_plots, cor = 0.5, method = "BHHR", data = . ) %>% 
  rename(exp_nam = id,
         logr = es, 
         logr_var = var) %>% 
  as_tibble()

## manipulating N plots -> same mean
df_c %>% 
  filter(exp_nam == "DUKE") %>% 
  mutate(n_plots = ifelse(Sampling_Year < 2000, n_plots, 2*n_plots)) %>% 
  mutate( id = exp_nam ) %>% 
  MAd::agg( id = id, es = logr, var = logr_var, n.1 = n_plots, n.2 = n_plots, cor = 0.5, method = "BHHR", data = . ) %>% 
  rename(exp_nam = id,
         logr = es, 
         logr_var = var) %>% 
  as_tibble()

## using rma.mv
out_meta <- df_c %>% 
  filter(exp_nam == "DUKE") %>% 
  mutate( id = exp_nam ) %>% 
  metafor::rma.mv( logr, logr_var, method = "REML", control = list(stepadj=0.3), data = .)
tibble(
  exp = "DUKE",
  logr = out_meta$b[1,1],
  logr_var = (out_meta$se * sqrt(out_meta$k))^2
  )

# df_c_agg %>% 
#   filter(exp_nam == "DUKE")
# 
# df_c_agg2 %>% 
#   filter(exp_nam == "DUKE")
```

Using `escalc()`, this now yields a value and standard error for each experiment.
```{r}
df_c_agg %>% 
  knitr::kable()
```

## Meta analysis

Now, we summarise that across multiple experiments to get a meta analysis of effect sizes, treating experiments as a random factor, and no moderators accounted for.

```{r}
out_meta <- df_c_agg %>% 
  metafor::rma.mv( logr, logr_var, method = "REML", random = ~ 1 | exp_nam, slab = exp_nam, control = list(stepadj=0.3), data = . )
```



Standard "forest plot".

```{r}
metafor::forest(out_meta, xlab="Log Response Ratio", mlab="", xlim=c(-1,1), cex=0.5)
```

Some other nice plot, showing a box with the confidence interval of the meta-analytic estimate.

```{r}
out_meta_scaled <- predict( out_meta, transf=exp )

df_box <- tibble(
  varnam = "anpp", 
  middle = out_meta$b[1,1], 
  ymin   = out_meta$ci.lb, 
  ymax   = out_meta$ci.ub,
  
  middle_scaled = out_meta_scaled$pred, 
  ymin_scaled   = out_meta_scaled$ci.lb, 
  ymax_scaled   = out_meta_scaled$ci.ub
)

df_c_agg %>%
  ggplot( aes(x = varnam, y = logr)) +
  geom_jitter( color = rgb(0,0,0,0.3), aes( size = 1/logr_se ), position = position_jitter(w = 0.2, h = 0) ) +
  geom_crossbar( data = df_box, aes(x = varnam, y = middle, ymin = ymin, ymax = ymax), fill = "grey80", alpha = 0.6, width = 0.5 ) +
  geom_hline( yintercept = 0.0, size = 0.5 ) +
  labs(x = "", y = "Log Response Ratio", size = expression(paste("Error"^{-1}))) +
  coord_flip() +
  ylim(-1,1)
```